Bring a large pot of lightly salted water to a boil; cook the rotini at a boil until tender yet firm to the bite, about 8 minutes; drain. Rinse with cold water until completely cooled; drain.
Mix pasta, eggs, artichoke hearts, celery, bell pepper, onion, ham, shrimp, peas, Cheddar cheese, Monterey Jack cheese, pickle, and olive together in a large bowl.
Whisk sour cream, mayonnaise, apple cider vinegar, sugar, ranch dressing mix, mustard, and hot pepper sauce together in a separate bowl; season with salt and black pepper.
Drizzle dressing over salad and toss to coat. Cover bowl with plastic wrap and chill in refrigerator 3 hours to overnight. Stir enough of the reserved artichoke marinade into the salad so it is just moistened before serving.